Bad link. FFS ALWAYS check if the links you post anywhere works! - I'm senior webdev and know the importance of always checking posted links. Learned the hard way.

I can with wizardry deduct the right url from the bad double url, but would be better if the link is corrected so anyone can view the link you posted.

EDIT: (If) you can not edit the OP then delete it and make new better one.

EDIT2: I need to register to read the paper!

Check Now

Did you mean to post an explanation of your understanding of the paper?

Sir, firstly thanks for responding.

I already have implemented this as a working program. But now I am enhancing it, and I have some feeling that I somehow am missing something from the paper, and not understanding it properly.

For example:

The equations [2, 4, 6, 8, 10, 15-18] in pages 3, 4 and 5

The training of the model with generated features with Linear LSE mentioned in page 6-7

And section B Local pixel difference descriptor, para 2 regarding directions. And it's related figures, Figure 3(a,b).

If you can explain these things, i can effectively understand your explanation and ask my doubts wrt my present work on this paper, with code.

Reply to edit 2 : that's why i sent u the previous link, which is from sci-hub.se

I think it's better if you ask specific questions, rather than ask people to explain the whole thing. The explanation in the paper seems pretty clear to me already...

[deleted]

Explain me equations 2 and 4 sir

How to design the identity matrices

So what are you asking?

Sir, firstly thanks for responding.

I already have implemented this as a working program. But now I am enhancing it, and I have some feeling that I somehow am missing something from the paper, and not understanding it properly.

For example:

The equations [2, 4, 6, 8, 10, 15-18] in pages 3, 4 and 5

The training of the model with generated features with Linear LSE mentioned in page 6-7

And section B Local pixel difference descriptor, para 2 regarding directions. And it's related figures, Figure 3(a,b).

If you can explain these things, i can effectively understand your explanation and ask my doubts wrt my present work on this paper, with code.

How can anyone answer this?

If you are wanting people to tell you if you've understood it correctly, you need to tell us what your understanding is.

Ok I'll ask you exactly what i don't understand.

In equations 2 and 4 there is I which represents Identity matrix right?

So if let's say l = 2 and N = 7

Now will the shift matrix be like

[ 0 0 0 0 0 1 0 ]
[ 0 0 0 0 0 0 1 ]
[ 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 ]
[ 1 0 0 0 0 0 0 ]
[ 0 1 0 0 0 0 0 ]

If yes, then

[ I  -I ]
[-I   I ]

Should be of the form,

[ 1 0 0 0 0 -1 0 ]
[ 0 1 0 0 0 0 -1 ]
[ 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 ]
[ -1 0 0 0 0 1 0 ]
[ 0 -1 0 0 0 0 1 ]

Or

[ 1 0 0 0 0 -1 0 ]
[ 0 1 0 0 0 0 -1 ]
[ 0 0 1 0 0 0 0 ]
[ 0 0 0 1 0 0 0 ]
[ 0 0 0 0 1 0 0 ]
[ -1 0 0 0 0 1 0 ]
[ 0 -1 0 0 0 0 1 ]

?

Be it horizontal shift or vertical shift.

And what do they mean by rotations here : 0°, 45°, 90°, 135° ?

Because I'm extending this idea, so I am asking community help, perspectives, opinions and understandings, so I may not be wrongly understanding math.

Ok I'll ask you exactly what i don't understand.

In equations 2 and 4 there is I which represents Identity matrix right?

So if let's say l = 2 and N = 7

Now will the shift matrix be like

[ 0 0 0 0 0 1 0 ]
[ 0 0 0 0 0 0 1 ]
[ 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 ]
[ 1 0 0 0 0 0 0 ]
[ 0 1 0 0 0 0 0 ]

If yes, then

[ I  -I ]
[-I   I ]

Should be of the form,

[ 1 0 0 0 0 -1 0 ]
[ 0 1 0 0 0 0 -1 ]
[ 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 ]
[ -1 0 0 0 0 1 0 ]
[ 0 -1 0 0 0 0 1 ]

Or

[ 1 0 0 0 0 -1 0 ]
[ 0 1 0 0 0 0 -1 ]
[ 0 0 1 0 0 0 0 ]
[ 0 0 0 1 0 0 0 ]
[ 0 0 0 0 1 0 0 ]
[ -1 0 0 0 0 1 0 ]
[ 0 -1 0 0 0 0 1 ]

?

Be it horizontal shift or vertical shift.

And what do they mean by rotations here : 0°, 45°, 90°, 135° ?

Because I'm extending this idea, so I am asking community help, perspectives, opinions and understandings, so I may not be wrongly understanding math.

Yes, I is the identity matrix.

The shift matrix, H, will not have a row or column with only zeros in it. If l is 2 and N is 7 then H(1, 3) (1 based) will be a 1 and the start of a diagonal.

You have similarly misunderstood equation 4. There will not be a row or column with only 0s in it.

The authors do not mention rotation at all in this paper. They do mention that gradients are computed along those directions by the pixel differences.

Please see dm

Much better to keep going here. Others can see and learn and/or contribute. Everyone is better off.

Do you have more questions?

Yes

> Yes, I is the identity matrix.

> The shift matrix, H, will not have a row or column with only zeros in it. If l is 2 and N is 7 then H(1, 3) (1 based?) will be a 1 and the start of a diagonal.

> You have similarly misunderstood equation 4. There will not be a row or column with only 0s in it.

Hl is this

[ 0 0 0 0 0 1 0 ]
[ 0 0 0 0 0 0 1 ]
[ 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 ]
[ 1 0 0 0 0 0 0 ]
[ 0 1 0 0 0 0 0 ]

I - Hl is ?

[ 1 0 0 0 0 -1 0 ]
[ 0 1 0 0 0 0 -1 ]
[ 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 ]
[ -1 0 0 0 0 1 0 ]
[ 0 -1 0 0 0 0 1 ]

Or

[ 1 0 0 0 0 -1 0 ]
[ 0 1 0 0 0 0 -1 ]
[ 0 0 1 0 0 0 0 ]
[ 0 0 0 1 0 0 0 ]
[ 0 0 0 0 1 0 0 ]
[ -1 0 0 0 0 1 0 ]
[ 0 -1 0 0 0 0 1 ]

?

Show me how the matrix is written

And elaborate this:

> The authors do not mention rotation at all in this paper. They do mention that gradients are computed along those directions by the pixel differences.

I dont follow what you are showing with those matrices. You should actually ask a question.

Are you stating what H x I is? If so, you are using the same definition in your original question which i just said was wrong. I could have been more specific about H: each row and xolumn will have exactly one occurance of a 1 and N-1 zeros.

H =

0 0 1 0 0 0 0

0 0 0 1 0 0 0

0 0 0 0 1 0 0

0 0 0 0 0 1 0

0 0 0 0 0 0 1

1 0 0 0 0 0 0

0 1 0 0 0 0 0

for l =2,N=7

Do you know how to subtract matrices from one another? The second and third matrix you show suggests you don't.

Im not sure what to elaborate on regarding the rotation that the authors dont mention in their paper. I could talk for hours about rotations, pixel differences, numerical gradients etc. Im not just going to ramble on without context. What do you want to know?

I am asking what is

I - H is?

I get the same H as you say, but what is the matrix we get after I - H? Is it a mirror of H? As in paper, they said

I  -I
-I  I

So, the I in I-H is, normal identity matrix where major diagonal elements are 1 or is it mirror of H

The identity matrix can be different sizes:

https://en.wikipedia.org/wiki/Identity_matrix

As for the rotations, it's in reference to the top of figure 3 and the position of the blue and red pixel.

I replied below.

What do you mean by “mirror of H"? I is always the identity matrix here. Why do you think it could be the "mirror" of H?

So I - HL will be

[ 1 0 0 0 0 -1 0 ]
[ 0 1 0 0 0 0 -1 ]
[ 0 0 1 0 0 0 0 ]
[ 0 0 0 1 0 0 0 ]
[ 0 0 0 0 1 0 0 ]
[ -1 0 0 0 0 1 0 ]
[ 0 -1 0 0 0 0 1 ]

This. And same goes for I - VL

Fine.

What do they mean by those rotations?

So how is rotation explained in the paper? Like which equations I should look into?

I would Like to show you my implementation of this paper, to how it acts on images.

So, I can ask you more on what exactly my issue is

It's not, they're just explaining the positioning of the pixels in the figure.